MalinC's GeoGebra-book

Malin Christersson, Midhun S Menon, Jan 25, 2019

All worksheets from http://www.malinc.se/math/ divided into chapters according to the menu at the site.

Table of Contents

  1. Linear Algebra
    1. Curve of Pursuit
    2. Translations along vector
    3. Definition of vector addition
    4. Construct the vector OP, using u and t
    5. Equation of a line through point along vector
    6. Equation of a line through two points
    7. Equation of a line, through two points
    8. Linear transformations
    9. Reaching a point in the Cartesian plane
    10. Rotating cube
    11. Vector subtraction and bound vectors
    12. Transformed graph
    13. w defined by the basis vectors u and v.
    14. Triangles
  2. Trigonometry
    1. Addition formula for cosine
    2. Addition formula for sine
    3. Area law
    4. Aristarchus' distance to the sun
    5. Aryabhata's half chord
    6. Chords in ancient Greece
    7. Combined transformations
    8. Cosine rule for acute triangle
    9. Dilated trigonometric functions
    10. Epitrochoid
    11. Eratosthenes' radius of the earth
    12. Graphs of tangent and cotangent
    13. Hypotrochoid
    14. Inverse functions
    15. Inverse trigonometric functions
    16. Law of cosine using obtuse triangle
    17. Ptolemy and epicycles
    18. Sine and cosine
    19. Sun, earth and moon
    20. Tangent and cotangent
    21. The Sine theorem, ambiguous case
    22. Translated trigonometric functions
    23. Triangle definition of sine and cosine
    24. Triangle in unit circle
    25. Trigonometric functions using degrees
    26. Trigonometric functions using radians
    27. Trigonometric identities in unit circle
    28. Tycho Brahe's mural quadrant
    29. Sextant
    30. Stellar Parallax
    31. The sound of a sine function
    32. Play notes
    33. Play overtones
  3. Statistics
    1. Binomial and normal distribution
    2. Normal distribution
  4. Calculus
    1. Archimedes Pi
    2. Area function as antiderivative
    3. Derivative at point
    4. Derivative at point, absolute value of a function
    5. Derivative as function
    6. Derivative of a polynomial
    7. Derivative of exponential function
    8. Derivative of logarithmic function
    9. Derivative of sine and cosine
    10. Integral demonstration
    11. Limit of sin(x)/x
    12. s-t-diagram and v-t-diagram
    13. Step functions
    14. Cob web diagram
    15. Damped pendulum
    16. First order ODE
    17. First order ODE with slope field
    18. Cob web diagram and attracting fixpoints
  5. Functions
    1. Non-Cartesian cars
    2. Cartesian cars
    3. Annuity loan
    4. Slope
    5. Linear points
    6. Linear points rotated
    7. Linear and exponential growth
    8. Translation using vector notation
    9. Translate function using tool
    10. Completing the square
    11. Vertex form
    12. Parabola
    13. Explanation of parabola
    14. Focus of the parabola
    15. Other conics
    16. Polynomials
    17. Quadratic and line
    18. Cubic and quadratic
    19. Composite functions
    20. Domain and range
    21. Inverse functions
  6. Geometry
    1. Quadrilaterals
    2. Triangles
    3. Pattern of Quadrilaterals
    4. Pattern of circles
    5. Transformations
    6. Translation
    7. Reflection
    8. Rotation
    9. Dynamic tessellation made of points placed on triangles
    10. Symmetries - reflection and rotation
    11. Shapes reflected in circles
    12. Circle mirror
    13. Make copies
    14. Copy from triangle along line
    15. Fractions as parts of squares
    16. Fractions as parts of circles.
    17. Positive fractions on the number line
    18. Negative fractions on the number line
    19. Multiply unit fractions
    20. Multiply fractions
    21. Area of triangle
    22. Area of a parallelogram
    23. Area of trapezium
    24. Summary of polygon areas
    25. Area of a circle
    26. Angle sum of a triangle
    27. Alternate angles at parallel lines
    28. Corresponding angles at parallel lines
    29. Vertical angles
    30. Exterior angle of a triangle
    31. Summary - Angles
    32. Two angles in triangle
    33. Sun, earth and moon
    34. Corollary of proportionality theorem
    35. Triangle proportionality theorem
    36. Angle bisector theorem
    37. Similar Triangles, exercise 1
    38. Triangles, exercise 2
    39. Apollonius Circles
    40. Square inscribed in triangle
    41. Midpoint & distance
    42. Strandbeest
    43. Points in triangle
    44. Trisect segment
    45. Angles along rays.
    46. Angle sum of a triangle
    47. The Pythagorean theorem
    48. Pythagorean theorem jigsaw puzzle
  7. GeoGebra Tutorial
    1. Interactive GeoGebra logo
    2. Pentagram
    3. Dragging test
    4. Demo of construction protocol
    5. Ruler and compass construction
    6. Pythagoras' Theorem showing numerical values
    7. Rotations, reflections, translations
    8. Animated Tessellated Pythagoras' Theorem Jigsaw Puzzle
    9. Aristotle's Wheel Paradox
    10. Measuring angles
    11. Sun, earth and moon
    12. Cats on ladder
    13. Cat on Ladder
    14. Möbius Transformations of Doyle Circles
    15. Complex mappings of a circle
    16. Complex mappings of a line
    17. Mobius transformations
    18. Points and vectors
    19. Polar coordinates
    20. Clock
    21. Pool Table
    22. A general cubic function
    23. Input box and composite functions
    24. Riemann sums
    25. Polar coordinates demo
    26. Implicit heart and smiley
    27. Lissajou curve
    28. Anaglyphic 3D Lissajou
    29. Ellipse or hyperbola
    30. Parabola made using spreadsheet
    31. Symmetries made using lists
    32. Infinitely many stars
    33. Button demonstration - move point
    34. Button demonstration
  8. Non-Euclidean Geometry
    1. Hyperbolic tools - Poincaré disc

1.

Linear Algebra

  • 1. Curve of Pursuit
  • 2. Translations along vector
  • 3. Definition of vector addition
  • 4. Construct the vector OP, using u and t
  • 5. Equation of a line through point along vector
  • 6. Equation of a line through two points
  • 7. Equation of a line, through two points
  • 8. Linear transformations
  • 9. Reaching a point in the Cartesian plane
  • 10. Rotating cube
  • 11. Vector subtraction and bound vectors
  • 12. Transformed graph
  • 13. w defined by the basis vectors u and v.
  • 14. Triangles

1.1.

Curve of Pursuit

Five ants chasing each other.[br]Move the big white dots!
– Malin Christersson

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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1.11.

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1.12.

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1.13.

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1.14.

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2.

Trigonometry

  • 1. Addition formula for cosine
  • 2. Addition formula for sine
  • 3. Area law
  • 4. Aristarchus' distance to the sun
  • 5. Aryabhata's half chord
  • 6. Chords in ancient Greece
  • 7. Combined transformations
  • 8. Cosine rule for acute triangle
  • 9. Dilated trigonometric functions
  • 10. Epitrochoid
  • 11. Eratosthenes' radius of the earth
  • 12. Graphs of tangent and cotangent
  • 13. Hypotrochoid
  • 14. Inverse functions
  • 15. Inverse trigonometric functions
  • 16. Law of cosine using obtuse triangle
  • 17. Ptolemy and epicycles
  • 18. Sine and cosine
  • 19. Sun, earth and moon
  • 20. Tangent and cotangent
  • 21. The Sine theorem, ambiguous case
  • 22. Translated trigonometric functions
  • 23. Triangle definition of sine and cosine
  • 24. Triangle in unit circle
  • 25. Trigonometric functions using degrees
  • 26. Trigonometric functions using radians
  • 27. Trigonometric identities in unit circle
  • 28. Tycho Brahe's mural quadrant
  • 29. Sextant
  • 30. Stellar Parallax
  • 31. The sound of a sine function
  • 32. Play notes
  • 33. Play overtones

2.1.

Addition formula for cosine

Change the angles to see the cases in all four quadrants.
– Malin Christersson

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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2.10.

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2.11.

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2.12.

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2.13.

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2.14.

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2.15.

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2.16.

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2.17.

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2.18.

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2.19.

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2.20.

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2.21.

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2.22.

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2.23.

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2.24.

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2.25.

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2.26.

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2.27.

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2.28.

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2.29.

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2.30.

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2.31.

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2.32.

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2.33.

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3.

Statistics

  • 1. Binomial and normal distribution
  • 2. Normal distribution

3.1.

Binomial and normal distribution

Change the sliders!
– Malin Christersson

3.2.

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4.

Calculus

  • 1. Archimedes Pi
  • 2. Area function as antiderivative
  • 3. Derivative at point
  • 4. Derivative at point, absolute value of a function
  • 5. Derivative as function
  • 6. Derivative of a polynomial
  • 7. Derivative of exponential function
  • 8. Derivative of logarithmic function
  • 9. Derivative of sine and cosine
  • 10. Integral demonstration
  • 11. Limit of sin(x)/x
  • 12. s-t-diagram and v-t-diagram
  • 13. Step functions
  • 14. Cob web diagram
  • 15. Damped pendulum
  • 16. First order ODE
  • 17. First order ODE with slope field
  • 18. Cob web diagram and attracting fixpoints

4.1.

Archimedes Pi

– Malin Christersson

4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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4.7.

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4.8.

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4.9.

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4.10.

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4.11.

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4.12.

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4.13.

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4.14.

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4.15.

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4.16.

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4.17.

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4.18.

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5.

Functions

  • 1. Non-Cartesian cars
  • 2. Cartesian cars
  • 3. Annuity loan
  • 4. Slope
  • 5. Linear points
  • 6. Linear points rotated
  • 7. Linear and exponential growth
  • 8. Translation using vector notation
  • 9. Translate function using tool
  • 10. Completing the square
  • 11. Vertex form
  • 12. Parabola
  • 13. Explanation of parabola
  • 14. Focus of the parabola
  • 15. Other conics
  • 16. Polynomials
  • 17. Quadratic and line
  • 18. Cubic and quadratic
  • 19. Composite functions
  • 20. Domain and range
  • 21. Inverse functions

5.1.

Non-Cartesian cars

Change t to let the cars race!
– Malin Christersson

5.2.

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5.3.

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5.4.

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5.5.

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5.6.

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5.7.

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5.8.

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5.9.

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5.10.

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5.11.

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5.12.

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5.13.

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5.14.

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5.15.

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5.16.

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5.17.

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5.18.

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5.19.

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5.20.

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5.21.

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6.

Geometry

  • 1. Quadrilaterals
  • 2. Triangles
  • 3. Pattern of Quadrilaterals
  • 4. Pattern of circles
  • 5. Transformations
  • 6. Translation
  • 7. Reflection
  • 8. Rotation
  • 9. Dynamic tessellation made of points placed on triangles
  • 10. Symmetries - reflection and rotation
  • 11. Shapes reflected in circles
  • 12. Circle mirror
  • 13. Make copies
  • 14. Copy from triangle along line
  • 15. Fractions as parts of squares
  • 16. Fractions as parts of circles.
  • 17. Positive fractions on the number line
  • 18. Negative fractions on the number line
  • 19. Multiply unit fractions
  • 20. Multiply fractions
  • 21. Area of triangle
  • 22. Area of a parallelogram
  • 23. Area of trapezium
  • 24. Summary of polygon areas
  • 25. Area of a circle
  • 26. Angle sum of a triangle
  • 27. Alternate angles at parallel lines
  • 28. Corresponding angles at parallel lines
  • 29. Vertical angles
  • 30. Exterior angle of a triangle
  • 31. Summary - Angles
  • 32. Two angles in triangle
  • 33. Sun, earth and moon
  • 34. Corollary of proportionality theorem
  • 35. Triangle proportionality theorem
  • 36. Angle bisector theorem
  • 37. Similar Triangles, exercise 1
  • 38. Triangles, exercise 2
  • 39. Apollonius Circles
  • 40. Square inscribed in triangle
  • 41. Midpoint & distance
  • 42. Strandbeest
  • 43. Points in triangle
  • 44. Trisect segment
  • 45. Angles along rays.
  • 46. Angle sum of a triangle
  • 47. The Pythagorean theorem
  • 48. Pythagorean theorem jigsaw puzzle

6.1.

Quadrilaterals

Dynamic demonstration of various quadrilaterals.[br]Drag the filled points!
– Malin Christersson

6.2.

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6.3.

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6.4.

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6.5.

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6.6.

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6.7.

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6.8.

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6.9.

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6.10.

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6.11.

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6.12.

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6.13.

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6.14.

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6.15.

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6.16.

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6.17.

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6.18.

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6.19.

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6.20.

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6.21.

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6.22.

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6.23.

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6.24.

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6.25.

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6.26.

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6.27.

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6.28.

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6.29.

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6.30.

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6.31.

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6.32.

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6.33.

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6.34.

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6.35.

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6.36.

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6.37.

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6.38.

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6.39.

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6.40.

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6.41.

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6.42.

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6.43.

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6.44.

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6.45.

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6.46.

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6.47.

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6.48.

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7.

GeoGebra Tutorial

  • 1. Interactive GeoGebra logo
  • 2. Pentagram
  • 3. Dragging test
  • 4. Demo of construction protocol
  • 5. Ruler and compass construction
  • 6. Pythagoras' Theorem showing numerical values
  • 7. Rotations, reflections, translations
  • 8. Animated Tessellated Pythagoras' Theorem Jigsaw Puzzle
  • 9. Aristotle's Wheel Paradox
  • 10. Measuring angles
  • 11. Sun, earth and moon
  • 12. Cats on ladder
  • 13. Cat on Ladder
  • 14. Möbius Transformations of Doyle Circles
  • 15. Complex mappings of a circle
  • 16. Complex mappings of a line
  • 17. Mobius transformations
  • 18. Points and vectors
  • 19. Polar coordinates
  • 20. Clock
  • 21. Pool Table
  • 22. A general cubic function
  • 23. Input box and composite functions
  • 24. Riemann sums
  • 25. Polar coordinates demo
  • 26. Implicit heart and smiley
  • 27. Lissajou curve
  • 28. Anaglyphic 3D Lissajou
  • 29. Ellipse or hyperbola
  • 30. Parabola made using spreadsheet
  • 31. Symmetries made using lists
  • 32. Infinitely many stars
  • 33. Button demonstration - move point
  • 34. Button demonstration

7.1.

Interactive GeoGebra logo

Drag the points!
– Malin Christersson

7.2.

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7.3.

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7.4.

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7.5.

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7.6.

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7.7.

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7.8.

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7.9.

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7.10.

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7.11.

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7.12.

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7.13.

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7.14.

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7.15.

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7.16.

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7.17.

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7.18.

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7.19.

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7.20.

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7.21.

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7.22.

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7.23.

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7.24.

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7.25.

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7.26.

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7.27.

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7.28.

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7.29.

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7.30.

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7.31.

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7.32.

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7.33.

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7.34.

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8.

Non-Euclidean Geometry

  • 1. Hyperbolic tools - Poincaré disc

8.1.

Hyperbolic tools - Poincaré disc

Move the points! Use the hyperbolic tools!

How to construct the tools is shown at [url]http://www.malinc.se/math/noneuclidean/poincarediscen.php[/url]
– Malin Christersson

Information